Can somebody explain the notation $f \in C^4$

Question

To give some context the full question is:

Suppose $f \in C^4$ in a interval containing the root $\alpha$ and that Newton’s method gives a sequence of iterates $\{x_k\}$, $k = 0, 1, 2, \dots$ which converge to $\alpha$. Show that Newton’s method is at least quadratically convergent to $\alpha$ if $f'(\alpha) \ne 0$. What is $C^4$ here?

Answer 1

The set of $4$ times continuously differentiable functions (i.e. the 4th derivative exists and is continuous).

http://mathworld.wolfram.com/C-kFunction.html